Multi-stage stochastic fluid models for congestion control

•We present multi-stage stochastic fluid models for congestion control.•These models are driven by applications in telecommunications and manufacturing.•We use elegant matrix-analytic methods and direct analysis methods.•We derive efficient methodology for the transient and stationary analysis.

We consider multi-stage stochastic fluid models (SFMs), driven by applications in telecommunications and manufacturing in which control of the behavior of the system during congestion may be required. In a two-stage SFM, the process starts from Stage 1 in level 0, and moves to Stage 2 when reaching threshold b2b2 from below. Stage 1 starts again when reaching threshold b1b2B>b2. Finally, we discuss a generalization to multi-stage SFMs. We use matrix-analytic methods and derive efficient methodology for the analysis of this class of models.